Capture in Regime of a Trapped Motion with Further Inelastic Collision for <i>Finite-Sized</i> Asteroid in ER3BP

Abstract

The application of a modern solving algorithm or method of resolving dynamical equations for small projectile of finite sizes orbiting to be captured in a trapped zigzaging oscillations on orbit around the another large asteroid and in a further inelastic colliding scenario with him (using a formulation of the elliptic restricted three-body problem, ER3BP) is studied semi-analytically. Herein, two primaries MSun and mp (mp MSun) revolve around their barycenter on Keplerian orbits with low eccentricities. A smaller body (projectile for attacking a large asteroid) is supposed to be a solid, almost symmetric ellipsoid, having the gravitational potential of the MacCullagh type. Our aim is to develop a previously introduced solving procedure and to investigate the updated dynamics of the projectile captured to a trapped dynamical resonance, thereby having the inelastic collision of a small projectile orbiting on quasi-stable elliptic orbits around the large asteroid, mp.

Keywords

• dynamics of finite-sized satellite
• rotation of finite-sized satellite
• elliptic restricted three-body problem, ER3BP
• trapped motion of satellite
• gravitational potential of MacCullagh type
• quasi-stable elliptic orbit